The River Model of General Relativity

[@ScienceClicEN]

I'm astonished by how good the visuals are! Great video as always!

[@cykkm]

Have you perchance received a reference to the paper I sent you a couple weeks back? The river model even handles Kerr spacetime.

[@ScienceClicEN]

@@cykkm Oh I had missed your email I just found it! Yes actually after making my video on this topic, I discovered that the river model was actually a thing, and that it's actually very useful in many situations, especially when studying black holes. It's funny because Andrew J. S. Hamilton who co-published the paper you sent me actually advised me on my video about falling into a black hole. Another thing the river model is good for is gravitational waves : they can be viewed as a sort of waves within the river, that stretch and squeeze the spaces between the rest masses that form the inertial grid of space.

[@dialectphilosophy]

Thanks ScienceClic! Your channel deserves a HUGE shout-out since your videos were the first to originally tackle the River Model, and thus furnished us with the understanding from which we were able to make this video. We very much wanted to reference the amazing visuals you pioneered in your Visualizing General Relativity series and connect them explicitly to the river model -- but it proved too much for one video, and we're gonna save that for a future work! Also, hopefully we didn't butcher the pronounciation of "Painlevé" too badly. Best!

[@ScienceClicEN]

​@@dialectphilosophy Haha the pronunciation was actually pretty good :) Since I didn't know about the river model my video was very blurry when interpreting the "falling grid", you rectified that in yours which is much more rigorous and precise on what it does (and does not) represent!

[@-danR]

The physical concepts and the visual realizations with the nicely balanced sight-gags are truly astonishing. I don't know any other channel on any other topic that even comes close to the melding of such a diverse array of elements.

[@ibrahimsaleh3155]

I’ve honestly been trying to learn and visualize general relativity for years on KZbin and altho this “earth surface accelerating up in all directions” is the breaking point for all other videos, you’ve done a spectacular job with the explanation and the animation. I hope you reach a million subs. Uou just got one sub closer :)

[@dialectphilosophy]

Thank you so much -- appreciate the support and stay tuned!

[@abelmedina7879]

Yea recently O saw a Ted Talk on black holes where everything started making sense once I knew that space time flows! Before youtube videos would have space time being warped but not flowing. It makes it all make sense

[@houdadah803]

I still can’t imagine how earth surface can accelerate in all directions. For me this will cause it to explode.

[@waynerawlings8599]

If we imagine that the earth is made of particles (atoms, subatomic particles) those particles can be seen to expand together, so earth stays in one piece. Although the fact that some particles like electrons are supposedly point size, this seems impossible so maybe they have an event horizon like the blackhole

[@balabuyew]

If the speed of space against Earth surface is 11000 m/s as shown in video, then the surface is NOT accelerating, it moves in space with CONSTANT speed. So, the video is logically inconsistent with itself.

[@jp-hh9xq]

MSEE here and lifelong physics enthusiast. I have been thinking about this video since you put it out and watched it about once a week since. I showed it to others. I'm fully won over by the river model based on this and other videos of yours. I never thought I would reject the standard warped spacetime explanation, yet here I am. I am especially taken by the formation of massive objects with the analogy plugging up the hole. Brilliant. Your explanation of, and even daring to cover, an alternative to the status quo is a brave, but I'm very glad you did it. After the first 5 mins of the first video of yours I watched, I was ready to leave an angry comment, but waited until the end and had to watch again to punch any hole in the logic, but it was flawless. I deleted the comment. And have become a zealot for this theory now. Looking forward to more videos.

[@gabrielragum]

This video has answered all the pending questions I had about the equivalence principle and given me a tool to visualize GR like never before. Cheers.

[@Benlucky13]

I think the analogy is also useful to explain why information can't be sent out of a black hole. In subcritical water flow waves can move upstream against the current, even a low amount of energy tossing a small pebble in can still make upstream waves. But in super critical flow even the largest rock thrown overboard can't make a wave that moves upstream

[@alwaysdisputin9930]

yeah. Action Labs white hole video is really good for demonstrating this. When we pee into the sink it creates a circle called a hydraulic jump. This is because: 1) when the pee lands it flow very quickly towards the walls of the sink. 2) The wave rebounds & tries to reach the centre of the sink i.e. where the pee is landing. 3) However it can't reach the centre because the pee in 1) is too fast. 4) Therefore the wave gets stuck. It just stands there & looks like a circle. If you try to send morse code waves to the centre they will also get stuck. Thus we can't send information into a white hole. & if time is reversed the urine flies into our penises. & thus it is like a black hole.

[@sannyid]

Indeed! Theoretical physicist Bill Unruh discusses this in some of his work, arguing that the waterfall 's edge is a "sonic horizon" analogous to a black hole's event horizon. A fish that has fallen down the edge of a waterfall cannot send a message (in the form of a sound wave) upstream of the waterfall's edge/sonic horizon: their sound wave travels at a constant speed, but the waterfall sweeps the flowing water (and the sound wave traveling in it) down faster than the wave's speed. Analogously, an observer that has passed a black hole's event horizon cannot send a message (in the form of a light signal) outside (or "upstream") of this event horizon: their light signal travels at a constant speed, but the black hole sweeps the space (and the light signal traveling in it) in (or "down") faster than the signal's speed.

[@theltalpha]

​@@sannyid, I am by no means an expert on this topic, but I dare to say that the analogy, whereby the edge of a waterfall would correspond to the event horizon of a black hole, is wrong. The edge of the waterfall is rather an analogy for the centre of a black whole. The event horizon of a black hole in the river/waterfall model correponds to any point UPSTREAM, i.e. BEFORE the waterfall, where the flow of water is so high, that not the even the fastest (or highest accelerating) ship could prevent from inevitably being drifted towards the edge of the waterfall. (Actually, this is addressed in 8:29.)

[@terrylandess6072]

Light is the agent and enemy here. It gave us the knowledge of existence, but can't overcome it's limitations on which we make most all of our assumptions or theories. A waterfall is no longer an unbroken chain of molecules - put that water into a pipe with the same flow and it all changes.

[@Flesh_Wizard]

​@@alwaysdisputin9930a black hole is kinda like when someone unpisses

[@ВячеславВячеславыч-с7с]

This is the best physics explanation channel on KZbin!

[@jack.d7873]

How did I miss the release of this a month ago? This analogy, along with the visuals, creates powerful intuition. Brilliant communication 👏

[@Roberto-REME]

Outstanding explanation. for a long time I struggled understanding how the earth could possibly be expanding in all directions. Excellent use of graphics and thanks to you, I have a much better grasp of this concept.

[@zedred8075]

Beginning to feel sorry for the gravity Monkey. Another uniquely interesting and thoughtful take on this topic. Many thanks!

[@waynerawlings8599]

Yeah they should give him a parachute so he can pull the cord after he has free fallen for a while

[@cslamov]

Gravity Monkey and Shroedinger's cat should unionize

[@AlHearn]

These videos of yours are so refreshing and are a breakout from the usual explanations that you have already pointed out are flawed. We need fresh thinking and fresh explanations. So thank you.

[@janroose1]

Amazing content! Please keep it up!

[@dialectphilosophy]

Gosh -- thank you for your generosity and support, it means a lot to the channel!

[@notatakennick]

Your animations are getting ridiculously good. You absolutely deserve a million subs! Also this flowing space model is how I've visioned gravity for a while now but damn does it raise even more questions...

[@haniamritdas4725]

... with more and better answers ...

[@RobertoCarlos-tn1iq]

you actually think that the black holes are constantly devouring space? this guy makes it seem like there is an infinite amount of water. there isn't.

[@notatakennick]

​@@RobertoCarlos-tn1iqBro we don't even know what space is. We can only observe very subjective effects and play with our symbols. What I'm talking about is visualizing effects of gravity with moving coordinates of space. This might not have anything to do with real space, it's just a mental tool.

[@Ila_Aras]

​@@RobertoCarlos-tn1iqspace is infinite, so water is infinite. if you believe space is finite, and you believe in gravitational forces, then you believe that for some unknown reason, the universe as we know it, is not being sucked into the empty space where matter is not. But if space is not infinite, then there is no empty space past our universe, meaning the only logical explanation for how we exist, is that we somehow live on a sphere, where moving perfectly straight will eventually lead you to your original position. To make it simple, if space is not infinite, then space coordinates are an infinite reflection of itself.

[@WalterSamuels]

Love your videos. Thank you for the incredible work you do. The visuals and animations were incredible! Can tell you must have put a lot of work into this. So if this is indeed the case, does this mean that the space that travels through a black hole somehow gets evaporated back into the universe at some other point in space, like is the case for a river?

[@dialectphilosophy]

Hey, sorry for missing this earlier! But thank you for your support and your kind words :-) If we want to extrapolate the analogy and treat space as something physically real, then indeed the space must "vanish" somewhere. Newton actually proposed such a "mass-eat-space" theory of reality once in a letter he wrote, so such a possibility is not as new-sounding as it seems. Some proponents of the river interpretation conjecture that each proton in each atom functions as a sort of miniature black hole, so that the river, as it flows into a body of mass, slowly dissipates. There are number of other issues to be considered with such a model, but we certainly plan on exploring it further down the line!

[@notator]

@@dialectphilosophy I'd love to see the idea of space being annihilated by protons worked out more fully in an animation explaining why there's no gravity at the centre of the earth. Would the same process apply to black holes?

[@SmashXano]

Love it! You always predict the questions which come to the viewers minds and guide them step by step through the argument. This helps me a lot to visualize the pricipals of GR and therefor keep them in mind permanently. Thank you very much!

[@dialectphilosophy]

Well, tbh, this video was made mostly to respond to the deluge of questions we got in the comments section after our "Sky is Falling Up" and "True Cause" video, but glad it helped clarify things and thank you!

[@wafflepotato]

genuine questions for my confusion abt the analogy 1. where does the space go. Into the fourth (spacial?) dimension? Seems like a pretty big ontological burden for general relativity. 2. Is “space” destroyed when it reaches the center of earth? Is space generated elsewhere? Is space even that kind of thing? 3. Why does matter get stuck in the sinkhole? Why not just get sucked into wherever space is going? Excellent videos as always! One of the few physics channels i actually trust 😅

[@thedeemon]

it's only a mental image, space is not a material thing that goes anywhere, gets created or destroyed.

[@PSG_Mobile]

Good questions! I would add why spacetime "falls" towards matter?

[@AdenoidHynkelThe2nd]

3. Matter gets stuck because of (mainly electromagnetic) repulsion between the bits of matter. You could say that every bit of matter is like a little mobile space drain trying to flow into the other space drains, but ultimately being forced to keep a distance by repulsive forces.

[@juliavixen176]

The space, and time, don't "go anywhere" or even move at all.... those are arbitrary coordinates that we map onto a four dimensional shape (spacetime) that describes the "distance" between any two points in spacetime. Any arbitrary 4D chunk of spacetime will always have the same hypervolume, but some of the space and time edges will get longer or shorter when compared to an identically sized hypervolume of spacetime located next to any large concentration of mass (and energy). General relativity is literally just geometry. It's literally just describes a (4D) shape.

[@juliavixen176]

I should add... light, by definition, follows a straight line. And material objects, being held together with electrostatic forces (i.e. light) will consider a straight line to be whatever light is doing, and follow along with the light. As long as you observe light to be following a straight line in your own reference frame, you are therefore in an inertial reference frame. (Because your ruler and clock, the atoms of which are held together with light, are going to bend with the light, and never measure any bend. You need to compare with rulers and clocks located far away.)

[@ajorge_yul]

Thanks!

[@dialectphilosophy]

Thank you so much for your incredible generosity and support! It means a lot to the channel and to our continued study of these subjects!

[@chathuermadusanka1138]

This one is gold compared to your other videos ❤.

[@TwilightMysts]

I came up with this idea years ago. I call it "space-time evaporation", and see the mechanics somewhat like the hydrology cycle. Gravity is where water (space) evaporates, and then dark energy is where rain (space) falls down and refills the lake. The problem I ran into with the analogy is that in water, if you shut off the engine of the boat, you will quickly come to a stop relative to the water itself. But in space when you shut off the engine you instead maintain the same speed relative to the "water" rather than coming to a stop. While the change in perspective that you are stationary, and the ground is accelerating upward, is interesting, I do not (as yet) see it solving this problem.

[@Yash-Patel-28]

Same here, I also came up with this Idea years ago I call it "space time fluid (liquid)" Physicists call space-time fabric but space-time has more properties of liquid than fabric. By space -time fluid model we can also justify why objects with mass spin. Think of vortex,its the fastest way fluid can flow into something. So basically objects don't spin but the space-time fluid itself flow in circular way because it's the fastest way it can flow. (If you are having difficulty understanding or visualising then read context paragraph below) It's not just one thing, there are many things that can be answered by this model. Context: Think and try to visualise two different universes stitched together. First is just physical matter and the second one is the ocean of space-time fluid. Both universes(you can also say dimensions) affect each other. The first dimension of physical matter creates a 3D hole in the ocean of space-time fluid. And the space-time fluid moves matter with itself. Space-time fluid is like medium. Everything in it moves at the highest speed(we call it the speed of light but it's the speed of everything). The difference is that massless things use their whole speed to move through space so they don't have any speed left to move through time. So we say that time doesn't exist for them. Similarly objects with mass ideally move through only time and not through space but when they start moving through space their speed of moving through time decreases. Black holes and any other objects with mass are really holes that are sucking space-time fluid constantly.

[@Yash-Patel-28]

This model is also more suitable for phenomena like gravitational waves and other things.

[@Yash-Patel-28]

To visualise why gravity weakens as we go far away from objects: Let's take earth, imagine belts of 100 km around the earth (like archery targets). The closer the belt from earth, the faster the fluid flows. Because the volume of the closer belt is less so it drains faster. The far away belt has more volume because of more diameter so it drains slower.

[@Yash-Patel-28]

One more thing we can prove is why the core of the massive object spins faster. In the vortex, the inner part spins faster (fluid dynamics). Space-time is fluid and it creates vortex around massive objects so the center part of it spins faster. The core of the sun, earth and any other star spins faster than the outer layer.

[@Yash-Patel-28]

We cannot move through space-time fluid faster than the speed of light but if we find a way to move the fluid itself then faster than light travel will be possible.

[@LucGendrot]

To me this feels so much more intuitive than the "stretched sheet" model used in so many science classrooms

[@timjohnson3913]

As it turns out, it’s more expensive to create a whirlpool in a classroom

[@pascalguerandel8181]

I'm mesmerized... it's hypnotic..love your explanations...and have a better understanding of what is actually happening 🎉🎉

[@GuyAtTheSix]

This is by far the best channel on the subject. Keep up the good work!

[@dananorth895]

This is precisely how I've veiwed gravity and spacetime flux/flow since I was 15-16 years old (I'm 62 on the 15 in 2 days). With many of the same analogies, in the case of the river all objects all swept along relative to laminar partical flow of the river at the same rate of velocity. But if one were to restrict their movement all would feel the same force only as long as they had the same cross section/volume as resistance "force/weight" to the particle flow around them. This is analogous to all objects falling and accelerating at the same "rate" irregardless of differing masses, if restricted stationary each experiences an "emergent" effect of weight relative not to crossection/volume but their mass in a moving/collapsing field. There is much, much more to this. I'm subscribed and will have to watch your other videos now. Will comment along the way as there are interesting implications regarding energy itself and how it manifests/moves. Thanks for the link as well will investigate.

[@GizmoMaltese]

This is such a better analogy than then rubber sheet they always show us. The rubber sheet never explained why something standing still should fall towards a large mass.

[@haraldriegler6000]

Thanks for a video that explains this in a great way!

[@dialectphilosophy]

Thank you for your support, and glad it made a difference for you!

[@km76]

Question: So if the Earth is 'breaking apart' by thrusting outwards in all directions, and it happens that space is moving at just the right speed to keep the Earth in one piece, does that mean if the Earth were travelling much faster - it would then break apart - or if travelling slower would crush itself? And... if it were travelling at a presumed higher speed - does that suggest the Earth would suffer a type of spaghettification?

[@gaemr_o5147]

This is easily one of my favorite channels on youtube. keep it up man

[@thetenrings]

I literally thought out the space time like a fluid all my life like a river. FINALLY someone addressed this.

[@nektu5435]

Not sure what you mean but this isn't the first time anyone has used this analogy. Have you never tried searching the internet for this analogy?

[@thetenrings]

@@nektu5435 no not rlly tbh

[@timjohnson3913]

@@thetenrings Do you find it strange that you proclaimed “FINALLY someone addressed this” about a this that you never bothered Googling to see if it had been addressed?

[@thetenrings]

@@timjohnson3913I never saw it being discussed in youtube

[@QuentinLapointe]

On my side, I thought that the floor was accelerating up. I am happy this analogy was addressed too. What I don't get though is why the heavier the floor, the faster its acceleration towards us is? If the floor keeps accelerating towards us, why have we not reached the speed of light yet :p ?

[@Rick.Sanchez]

Thank your for these illustrative clarifications on topics dear to my heart!

[@-_Nuke_-]

I like that this channel sticks with special and general relativity. This is the reason I subscribed and you guys are the ONLY ONES addressing that river model. I won't claim that I understand everything but I have the feeling that more are coming to the for.

[@gauravrana9512]

Best Analogy till date I have came across -- Thanks @Dialect

[@dmarckos]

You've very brilliantly explained the science gravity without the math. I now understand it.

[@Leoo___]

So, this was what I really hoped you would go over was (I know it is an analogy, and a great one at that, but..) where does the sucked-up spacetime go? Like the water goes into the drain, where is the drain of an object with mass, and what happens to it when it goes down that drain?

[@TroyRubert]

Man, this really helped things click in my mind. Excellent video!

[@DynestiGTI]

Happy to see the video is back up, one of the best you've made so far, you outdid yourself with the visualisations. Love your GR series, I really hope to see you gain more subscribers in the future!

[@dialectphilosophy]

Thank you so much!

[@ivocanevo]

Thank you for making this intuition detailed and concrete. I feel like we may have the Grant Sanderson of physics here. On the edge of my seat for the next one... Subscribing!

[@dialectphilosophy]

Thank you for watching!

[@Ignisan_66]

Best explanation of general relativity I have ever seen. 👍👍 You are amazing.

[@jmcsquared18]

This might be your best video. You address the paradoxical question of what "the Earth is accelerating upwards" could mean. Though I still don't care for that language, your illustration of the river model as an explanation for this observation is beautiful. I'm still curious how the river model connects to the block model, which is what I usually employ. I think the block model is the most realistic with how relativity works, but I might have to admit that the river model is be exponentially easier to visualize haha.

[@jddang3738]

"the Earth is accelerating upwards" could be replaced with "the Earth is accelerating us up/outwards". Most people think acceleration = motion, but it's not, in general relativity. Proper acceleration is any force that causes an object to deviate from its geodesic.

[@jmcsquared18]

@@jddang3738 I think that would be more appropriate, actually. I even tell my physics 1 students that you don't feel your weight, you feel the normal force of the chair pushing on your butt. That's a familiar idea, the Earth pushing against you. In general relativity, you would "fall" in a straight line geodesic, but the Earth's surface gets in your way and that's what you feel when you're on the Earth.

[@dialectphilosophy]

Thank you for the kind words and for watching! There wasn't enough time in this video to address the connection to the spacetime-block view, but hopefully we'll get to it soon in another video. As to the point about acceleration = motion, it all depends on how you choose to view the concept of "motion" of course. If you interpret motion as the necessary consequence of a force, then the river view is rather indispensable. Indeed, one might argue that the assertion "acceleration causes an object to deviate from its geodesic" is nothing further than this view, just wrapped in mathematical lingo, since objects traveling along geodesics through spacetime are technically at rest in space. Of course, you could choose to define motion with respect to some globally stationary coordinate system, in which case spacetime curvature begins to look a whole lot like a regular force. The real problem seems to boil down to the fact that there appear to multiple ways to interpret GR, as a certain mathematical structure doesn't necessarily imply a unique singular interpretation of that structure.

[@jmcsquared18]

@@dialectphilosophy yeah that whole topic opens up quite the can of worms lol. Interestingly, it's similar to how there are many ways to interpret quantum mechanics. I always pictured general relativity as having a much clearer ontology than the quantum theory, but perhaps that was a naïve viewpoint. Of course, quantum mechanics is mathematically incomplete, as well as ontologically incomplete. But maybe relativity has a richer interpretation than I thought, since it's not just spacetime geometry we have to worry about, but also the observer and their coordinate choices. In any case, this is a fascinating pedagogical topic for physics professors to reflect upon when teaching relativity, and I'm excited for the next video!

[@pepegrillo9722]

Elaborating on something someone else posted in the comments, I think the "upwards" acceleration becomes completely intuitive: Imagine a disc floating big enough to no fit inside the river's drainage in the animations. That disc is equivalent to earth's matter pushing against each other's mass (the boats clogging the drain). Now each side of the disc is pushed by the river (accelerated) in the opposite direction... every opposite side from where water if flowing in, is accelerating at the same speed. It's so simple and beautiful.

[@salicazsali]

This channel is so good! You guys are seriously underrated with that sub count. I've seen better explanations from you guys than I have from some the larger channels such as PBS etc. No shade on them, but you guys are my favourite for this content.

[@xyalisaxanov4886]

Just wow, the quality of the explanation is superb. I lear very little from All other youtube channels.

[@coen226]

The information is so well laid out. Subscribed!

[@jaeimp]

One of the most enjoyable videos in science and math on YT. Question... If the fabric of spacetime is sinking into massive objects like planet Earth, much like a river falls in a waterfall, or a sink in a vector field, is the actual mass of planet Earth (the core, the crust, rocks, magma) an enormous "plug" stopping us from being sucked into some sort of black hole?

[@VernAfterReading]

Wow! I would love to see this applied to orbital mechanics. I think I get it: the "flow" inward gives you the centripetal acceleration you need to move in a circle/ellipse, and you only have to have constant velocity laterally for your given orbit (so no need for an engine, once you have the right lateral velocity). Things like Oberth Effect make sense too.

[@dlavod]

So technically, instead of us 'travelling throught space', space travels through us?

[@davidkeane1820]

Ive heard the ‘ground rushing up’ story before but this is a great way to understand how we stay neutral on the earth…well done for explaining it this way - thank you

[@ironbark88]

I love the way you explain and illustrate these complex concepts with simple analogies. You have a gift.

[@t.x3.064]

This is the best thing I have ever seen

[@nrosko]

Amazing thank you, this channel has become essential viewing.

[@arthurdurand4098]

At 15:03 why does the apple already have a speed relative to the ground = 11’000 m/s ? Shouldn’t it be 0 when we drop it, then it increases at 9.81m/s every seconds ?

[@M_1024]

It's written as "Velocity with respect to Apple" when it should really be "Velocity of the River of Space with respect to Apple" (or vice versa)

[@johnholme783]

This is one of the best videos I’ve seen on general relativity, it is spot on! It agrees with what professor Brian cox said in one of his dvd’s in wonders of the universe. What he actually said was that space literally flows like a river towards a black hole! Well done!

[@hugoballroom5510]

As usual the graphics are witty and the narration clear and concise. Great work. This feels a little like finishing up some the picture the GR/twins series has been developing, and i appreciate that the questions immediately come up about the interpretation. I am particularly wondering how a dynamic space interacts with matter. How does space-flow affect the matter in it? The "force" of Gravity used to be the cause. I am thinking of visualizations that involve perspectival shifts, like a Poincaré disk but inverted where the edge is the center. So that what changes with location is just a metric effect. The static milky way in the background briefly around 3:50 felt distinctly "Machian" or "Machist." Looking forward to the investigation.

[@aclearlight]

Bravo! Your work is both RELATIVELY and ABSOLUTELY awesome.

[@ducbao414]

I've been hooked on your channel since the Twin Paradox series. Been watching PBS Spacetime and History of the Universe (still love them) for a few years, I must say Dialect is in a class of its own. For me, it's your explanation and way of applying the equivalence principle and spacetime geometry that make Dialect the most mesmerizing and in-depth content on KZbin. I'm grateful for your channel.

[@dialectphilosophy]

thanks for your support! And we're returning to the Twin Paradox very soon (and we know we keep saying that, but this time we mean it)

[@ducbao414]

@@dialectphilosophy I'm eagerly waiting for it! In fact, all the content produced by Dialect has been exceptional, so I'm excited to see any content you make, whether it be in theoretical physics, logic, or philosophy.

[@jaktrip6093]

Aww, I was so proud of my idea that space curvature could actually be regarded as "spacetime flowing into mass" and then I learn this is an existing theory! In any case, THANK you. Yours is the first youtube channel I ever subscribed. Your way of looking at physics is so fresh and wonderful. I believe a deeper understanding of gravity, mass and energy are the key to further advancement in physics and your channel provides the best support for this journey that I have yet come across. There are a few things about the river model that bug me though: - the biggest break in analogy for me is that we imagine the river and the boat to be separate, while in the case of mass, the river and the boat are two sides of the same coin. How exactly does mass cause a river? Can we find an analogy for this part of the deal - anything similar that we can observe in nature where an object causes a flow into itself? - where does the space go? It is hard for me to imagine that space flows into mass and then ceases to exist. I can see a number of possible explanations like it is consumed by the mass as energy to sustain the swinging that define particles. But then, why does mass do this and other energy does not? Or maybe other energy also consumes fields but we don't experience it?

[@soopergoof232]

@jaktrip6093 wrote: >> "I was so proud of my idea that space curvature could actually be regarded as "spacetime flowing into mass" and then I learn this is an existing theory!" Congrads, but the same model has been deduced by a number of people worldwide, independently and without collaboration over the last century. It's just common sense and deductive reasoning like yours, simply letting gravity BE exactly what it appears to be and behaves as. Pure Occam's Razor stuff. Here's a recent paper by another such individual - henrylindner.net/Writings/BeyondNewtonPE.pdf >> "There are a few things about the river model that bug me though: - the biggest break in analogy for me is that we imagine the river and the boat to be separate, while in the case of mass, the river and the boat are two sides of the same coin. How exactly does mass cause a river?" Any gravitating mass (say the Earth) is a 'sink' or drain for the centripetally flowing "river" >> "Can we find an analogy for this part of the deal - anything similar that we can observe in nature where an object causes a flow into itself?" Sure. Think of air going into a vacuum cleaner, or down the throat of a carburetor. The flow is responding to a pressure gradient, flowing from higher to lower pressure. The Earth presents a pressure gradient in space itself, a lower-pressure 'sump' for gravitational spaceflow, powered by the higher ambient pressure of space itself. The resulting centripetal inflow is pictured in 3D briefly at 12:35 in the vid. And here comes the kicker - gravity is entirely a pressure-driven PUSH force; its perceived "pull" is a pseudo force like 'suction' or 'vacuum' (just as with the vacuum cleaner/carburetor analogy). >> "- where does the space go? It is hard for me to imagine that space flows into mass and then ceases to exist." That's almost always the first issue to come up. Is it like a California dry lake where the river just 'peters out'? Or like a Roach Motel?:-) Or what if ALL gravitational spaceflow inevitably ends up going into a black hole? And what if within all matter, there is a particular subatomic particle that's a micro-scale BH? What would qualify it as such? Well, it would have to be the most primal, most permanent and stable of all particles, and would have to be the seat of the strong nuclear force (aka 'quantum gravity'). And that would be the proton. All the protons within any gravitating mass would be where its collective inflow "goes to", besides going into all astrophysical BHs big and small. This is conjecture of course, but might provide some food for thought on where the stuff goes to. BTW, "curvature" would be code for the *rate of acceleration* of flowing space, aka the 'strength' or FORCE of gravity. 'Curvature' for Earth for instance, would be approx. 9.8m/s² (depending on altitude).

[@RalphEllis]

The river analogy. …err - you have just reinvented the aether…..! R

[@dritemolawzbks8574]

Stop it. We're in 2023, not the 1823. Go back and re-watch his videos on relativity, so that you can catch up with the rest of his audience.

[@dialectphilosophy]

That is a common objection against the River Model, that is creates a substantialist view of space. There are several further analyses to be made about such a statement, and we'll probably follow up on them in future videos.

[@markdelej]

This is great. A few questions: 1) why does space accelerate inwards towards the centre of mass of objects? 2) if space falls at 11,000m/s at earth’s surface then why does dropping something make it accelerate at 9.8m/s^2? There seems to be a friction between space and matter which based on the speed of the space river is what dictates how rapidly the object accelerates. 3) How come if you move through space at constant velocity there is no friction between you and space, but when space accelerates through you, it forces you to accelerate?

[@soopergoof232]

Dude! Those are SUPER excellent questions. 1.) Any gravitating mass is a 'sink' or drain, with all of 'space' being under extreme pressure, resulting in an *accelerating*, 'reverse starburst' flow into the zone (or point) of lowest pressure. 2.) Inflow velocity and acceleration-rate at a gravitator's surface depends on its mass. The greater the mass, the higher the inflow-rate, ergo higher gravity. The 'friction' you speak of is 100% the result of acceleration. With no acceleration, there is no 'friction' _irrespective of a spaceflow's actual velocity_. 3.) 'Space' is a perfect superfluid in the absence of any acceleration... same reason an object can coast frictionlessly thru space _at any velocity_ per Newton's first law. Space presents a viscosity/'friction' in the presence of any acceleration ¹. If space is accelerating thru an object's atomic lattice, it gives the object 'weight' (provided the object is prevented from falling). Release the object, and instantly it's weightless in freefall, simply "going with the flow". Conversely, when the lattice is being accelerated thru space, the very same 'viscous' effect causes inertia. Remove the acceleration, and the object coasts frictionlessly again, at its new velocity. In your three questions, you've hit on 'space' being an "acceleration-mediated quasi superfluid". This property underlies and unifies Newton's laws of inertia and conservation of momentum, Einstein's gravity/acceleration equivalence (monkey in rocketship), and the equivalence of gravitational and inertial mass. All in one tidy little package with a bow on top. 🎁 ¹. Under acceleration, the lattice comes under tension, resisting being 'stretched' in the axis of flow. This is the source of the 'viscous' effect. A rough analogy is seen in non-Newtonian fluids (like oobleck) in their stress-mediated variable viscosity.

[@surrealphysics]

So great!! I'm also a big fan of the river analogy! Excellent work!!! (And wow... So many Blender cycles too!!)

[@dialectphilosophy]

Haha thank you! Won't even begin to mention how many hours were wasted playing with the water simulator... never again!

[@surrealphysics]

@@dialectphilosophy not wasted! The product is at least well-appreciated!

[@daniel4647]

Wow, now it's actually making sense. I didn't really understand the idea that the ground was accelerating in the other videos, but it makes sense now. Thanks.

[@telotawa]

i like to imagine it like a narrow river with a big stick across it, and floating on your back on an inflatable pool toy or something, with your feet on the stick. you'd feel a force pushing on your feet, and you could jump up and fall back down, just like on a planet

[@nucolorized9051]

I like your analogy better than the one where the boat is using it's motor to stay in one place. Your analogy better represents a person standing on the Earth. In the 360° river analogy 10:40 we could imagine a floating ring over the drain. If the ring were too large to fit down the drain it would remain in one place. Then you could brace your feet against it and it would be like standing on a planet.

[@incognitospider330]

Yes but its wrong according to GR, the ground is not still like the stick or the ring, it moves outwards for some reason

[@gastonlagaffe9156]

This brilliant exposition needs a brilliant mind at its origin. Thank you, you got a new subscriber.

[@UgorGred]

we need this in all languages of the world

[@cykkm]

Oh wow! By pure chance I came across a paper 10.1119/1.2830526, 2008, Arxiv gr-qc/0411060 2006, developing this model. Just a couple weeks back! It becomes very interesting when the Kerr spacetime does the Lense-Thirring, it's not like a vortex in the draining bathtub-every point in the flowing space has the vorticity, but there is no vortex, the Kerr space still flows steadily! Amazing stuff, thanks for such an astounding animation! P.S. Yeah, the 1st author is the same Andrew Hamilton, ~ajsh, the same guy you've linked to.

[@dialectphilosophy]

We found that same paper during our research for this video! It was extremely enlightening. How we'd interpret the rotational vorticity without a global vortex is like having tiny "eddying" currents in your river... for instance, if you pass a floating stick over a very small eddy in your river, its rotation will change, but not its direction of flow, which produces the description that occurs in Hamilton's paper.

[@Keeykey]

This analogy makes me think that every massive particle is a tiny black hole that consumes a certain volume of space per second depending on it's mass.

[@juliavixen176]

Oh, you're about to run into some major problems when trying to combine Quantum Mechanics with Gravity...

[@Totaro17]

@@juliavixen176yeah, seems everyone has that problem. So, makes me think that’s he’s right.

[@StrangersIteDomum]

Miles Mathis charge recycling

[@axle.student]

Fortunately space-time would appear to be massless, so plenty of room at the singularity :P

[@mariosmourelatos9533]

Thanks again for the great video. What wasn’t clear though is how you can accelerate and maintain the same speed all the time? Acc dv/dt if dv = 0 then acc = 0

[@usermlgbzzcnm]

Great video as always!

[@jermsbestfriend9296]

Wow. I've been dreaming about this video for years. Thank you so much. ❤️❤️❤️❤️

[@petecurry4881]

Love your videos, I've been waiting for this one! - the inflow, river, and waterfall analogies all make perfect sense to me for describing gravity and the behavior of spacetime, but I'm still completely confused by this "pushing outward" thing. I understand that mass causes the inflow of spacetime but not why mass "pushes back" against that flow When you said the boats will be "forced to accelerate outwards," what do you mean forced? It looks like they're only being forced inwards by the inflow of spacetime. Why don't they just crunch up? Why does inert mass have any will or mechanism to accelerate against the inflow of spacetime? What is is causing the outward acceleration of the mass of the earth? Am I just just missing something in the explanation, or is this something fundamental about mass, that mass itself inherently pushes outwards? Is it because of the other 3 fundamental forces in particles and atoms? Perhaps that's what your next video will describe, keep up the great work it's much appreciated!

[@incognitospider330]

Same question

[@Vkonto]

Dude you have upped your game .. keep making these amazing videos

[@Astro_AmanJha]

This is perhaps the best KZbin video ever I saw on General Relativity. It's like you brought down our closed eyes thought expt into visual reality. From monkey sacrificing for us to river model, absolutely perfect. Being a Physics student from India, lot's of love, wishes and good health. I recommend your videos to all my friends and profs, and they all love it. Just speechless bro, ur efforts!!!! Hands down... To explain complex things in subtle manner is what makes this channel in the top lists of best ed channels alongside Veritasium, PBS, VSauce... Lot's of love and wishes

[@dialectphilosophy]

That makes us thrilled to hear! So glad our videos are helping!

[@N3PTUN3SOUL]

Whoa…I just came across your channel, and I’m literally mind blown…

[@shroomskaiev]

Great material, should be shown to students instead of the '' ball on a trampoline " analogy, for sure

[@FartKillerX]

Ball on a trampoline isn't that bad. It's way better for getting an intuitive understanding of gravitational waves.

[@timjohnson3913]

The physics teacher consulted the budget and turns out they didn’t have enough money to turn their classroom into a whirlpool.

[@realcygnus]

Superb content ! & animation / production

[@dosomething3]

amazing. However, unless water stretches, it is impossible for water to flow faster as you get closer to the waterfall.❤

[@timjohnson3913]

No, the waterfall and river source just needs to narrow the closer you get to the fall.

[@jddang3738]

@@timjohnson3913 The water volume right above the fall is usually shallower than the stream/river leading up to it.

[@juliavixen176]

@@jddang3738 It doesn't need to be shallower... when it isn't all the water falls out faster and you just have an empty valley or salt flat with a broad cliff, or something... this is more of a Geology thing, and the "waterfall" model of gravity is an analogy, and not a real waterfall.

[@dialectphilosophy]

Our depiction of a waterfall isn't very physically accurate, and was intended to create a picture which mirrored the linear picture of approaching a body of mass. Now, there are several reasons why water flows faster near the edge of a waterfall and the discussion of why that is, is actually quite illuminating for the river model. Unfortunately it was too much for one video, so it'll come up at a later date.

[@juleskurianmathew2398]

One of the best and true videos of the concept!

[@kulubot6534]

I'm early, love your videos. Especially when you destroy someone else's vid

[@lllinois]

Thank you, this video is amazing. So excited for you to get into more detail!

[@timjohnson3913]

A huge red flag with this idea is that we must assume matter is somehow attached to space, and when space is moving the matter must move along with it. It is far from clear how this interaction can work. When we travel through space, it’s not like we drag along the bits of space our matter sits on with us. Instead, traveling matter is moving into new bits of space (space atoms, if you like) as it travles. I would love to see Dialect provide the details as to how/why moving space would drag matter with it.

[@quanphung9966]

That's what coming up next

[@jddang3738]

It's just an analogy to help people understand the concept of how the Earth's surface, can be accelerating us up/outward. Notice in the video, nothing really moves towards the center of the mass until he drops a ring of particles around it, and another ring, and another ring, etc. It's the particles which are flowing like a river.

[@timjohnson3913]

@@jddang3738 Literally the first sentence in his description of the video: “Does space “flow” like a river?” It’s not just the particles bud; he’s claiming it’s the space that’s flowing and the particles are just floating along for the ride.

[@juliavixen176]

Inertia and "inertial reference frames" are what this is based on... and inertia is kinda non-intuitive if you've lived your whole life as a human on the surface of the Earth. I don't want to write a long comment here about Galileo and Newton's first law of motion... but mechanically inertia comes down to the subatomic particles that compose material objects being held together with electrostatic forces -- the electric force is essentially "light". You're body is partially made out of light, to put it bluntly. And when the light takes the same amount of time to travel between all of your atoms in every direction equally, you will measure yourself as being "at rest", i.e. in an inertial reference frame. If the light needs to travel a further distance through "space" in one direction than in other directions, you will measure this as acceleration, a "force". Newton's second law of motion is that anything which is not straight line motion through space is by definition involving acceleration (a force for constant mass). General relativity is curving the "straight line" path of light, and material objects fallow the path of light, because material objects are held together with "light".

[@dialectphilosophy]

How far can an analogy take us?... stay tuned...

[@Yezpahr]

The first expression of the monkey when it was still interacting with a falling apple and grid was foreshadowing the torture it was about to endure. Priceless mixture of science and humor.

[@OverwoundGames]

Or put simply "mass eats space" 🙃 I've been working on this idea for a while too and thinking about it at a quantum level has lead me to some interesting ideas and possibilities with mirror-verses, dark matter, the insides of black holes and possibly even anti-gravity (or an analogue of) - so will be interested to see where you go next with this ☺

[@patrickfle9172]

Same!

[@manueldaniel2371]

Have you consider to join that "sink" of space, where "mass eats space", wirh the opposite "source" in empty space (with no mass), where "space creates space", giving place to a number of phenomena, from universe accelerated expansion to limited speed of light (although photons seem to move instantaneously, with no time flowing)?

[@OverwoundGames]

@@manueldaniel2371 I've wondered whether the space is destroyed or separated off like droplets of water into their own separate universes, or into a shared parallel universe, perhaps with inverted spacial dimensions (a mirror-verse) - and that could have interesting implications for quantum-entanglement or a realm for dark matter to hide. As for space coming back into our dimensions causing expansion, I've seen it suggested that antimatter might expand space but I don't think that's possible, as it appears to falls the same as regular matter. An idea I prefer, inspired by holographic, information and simulation theories of the universe, is that as particles consist of information, in order for a quantum interaction to create a new particle, new space must be created to store it in, but perhaps when a particle is annihilated that space is left behind and not deleted. Think then of the interactions in the quantum foam, where photons split into electron-position pairs then recombine into photons, and this process could result in ever-expanding space. This could theoretically be tested if you could rapidly create and destroy antimatter underneath a super-sensitive scale or some other gravitational measure, but perhaps not in practice! 🙃

[@balabuyew]

To introduce acceleration (which is needed for "apparent gravitational force") the mass should eat space with more and more speed over time. So, it should eat more space in each next second compared to the corresponding previous second.

[@manueldaniel2371]

@@balabuyew I don't think so. Constant speed of "amount" of space eaten would transmit (in time) along 3-dimensional space (spherecally), resulting in a "space falling speed", in every point, inversely proportional to the square of the distance, just for geometrical reasons.

[@nicholasparkin6054]

Hi @dialect. First I want to say how revolutionary and unique your channel is, challanging mainstram perspectives that, whilst not being new "physics" per se, does exactly what modern physics needs, incorporates new philosophy into our physics. I have some questions: Is the river model of Space time equivalent to the curved model? Can curvature always be represented as flow, and flow as curvature? If so, does this mean we cannot say that our spacetime is curved or that it flows, but rather, what we observe is consistent with either veiw point?

[@nicholasparkin6054]

Or are you saying that they come together, that space flows along the curvature?

[@dialectphilosophy]

In this case, curvature serves as a description of a flowing system. So you can have the space flowing in euclidean space-time, or you can have "static" space but which gets sucked together via traveling on curved geodesics on a spacetime manifold. If those sound like very similar situations it's because ultimately yes, the two pictures are equivalent.

[@nicholasparkin6054]

@@dialectphilosophy Thank you for the swift reply. Well then this really begs the question, why do we tell students that 'matter curves spacetime' instead of introducing it first as 'space flows into matter'? The latter is so much easier to grasp, and then we can point out that, if you then create a picture from gluing every moment of 3d space together, this flowing is manifested as curvature. We can then point out that this interpretation can be reversed, with flow representing the curvature - which leads nicely into a discussion of the Heraclitean (which is in line with the flow view) vs the Parmenidean (which is more in line with the 4d curved manifold view) view of reality. This would have two advantages. 1) It would help students to realise that one must be careful to draw physical conclusions from models - as you rightly point out in many of your videos. 2) The flow view, to me at least, makes all of relatively completely intelligable. Let me ellaborate on that second point. The flow of space, along with the speed of light in space, understanding of wave mechanics (which you showed explains time dilation and length contraction), and the fact that cause and effect (equivalently information) ultimately flows via such waves, makes it all intelligible! No need to throw up our hands and say "it just doesn't make sense because our intuition is wrong" - that's nonsense! Is my reasoning correct? Thank you so much again dialect, please keep up the good work.

[@zohn-yq6wx]

Ok, we want to know what happens beyond the event horizon. First we need to know what happens outside the blackhole. A blackhole has a event horizon, a accretion disk and angular momentum. The blackhole spins hot plasma matter it catches from the galaxy in a accretion disk. As a result, that hot plasma matter gets converted into high energy particle blazers. And shot out in the form of cosmic jets at 99% of C. That is it's purpose. It's a matter energy converter. You might ask why ? Because if a galaxy like our milky-way had to much matter, it would only be a giant blackhole the size of the milky-way with no stars,planets, and we wouldn't be here on earth right now. In other words, this (M🔼(+E)=99% of C). The triangle is a science symbol delta means to convert to change something. Ok don't forget that blackhole equation. Now what happens below the event horizon that void ? For close to 50 years they said beyond the horizon all that star matter was crush to infinite density matter and was still matter, in other words this (M=M=singularity). But now they say there is no singularity no M. Now what happens beyond(below) the horizon. This is the equation ((event horizon = g)× (spacetime = tidal force)>(300,000 km/s) =(+E=C)^(+E🔼(-E)= (negative repulsive energy))= expansion rate of our round bubble or toros universe(the hubble constant).Remember 🔼= to convert, to change. In other words, +E beyond the event horizon is spaghettified(science term to stretch) by tidal forces traveling faster then C beyond the event horizon. To a Quantum State( the smallest possible energy particle, something we've never seen before, because we can't make a blackhole in a laboratory). That particle is negative repulsive energy -E. Not anti-gravity, because gravity is a gravity well, curved space-time. You might say why doesn't +E stay as +E after spaghettified. Because it would just start to clump up from a Quantum State and become plasma matter again. So, as negative repulsive energy -E. It will travel below the event horizon using tidal forces(spacetime)) and help our universe to continue to expand. So its a matter energy converter above and below the event horizon. Now time dilation it affects +E above the event horizon. It slows down the amount of +E that crosses the event horizon. Perhaps 1% of +E crossed the event horizon. But, you might say, how can the universe expand with just 1% of (-E). Because there are 2 trillion galaxies (with blackholes) in the observable universe and trillions more beyond the cosmic horizon(unseen galaxies) all those trillions of galaxies are converting matter to positive +E and - E. .😎.

[@aravinth007vt]

Thank you for the video first all. I always had this thought like in most of the diagram they show, that the earth sitting on a sheet like dented images to be wrong. You have shown it perfectly. Including the three dimensions view.

[@Airatgl]

Very interesting to see how this model shows the flow of spacetime with multiple masses. And how dark energy involved in it.

[@dexter8705]

There was nothing to do with dark energy or spacetime in this video.. just space.

[@mategido]

Not many things can increase my fear of instant death space stuff like a black hole, but you just did it, awesome video

[@thedeemon]

There's one huge problem with this analogy. A flowing river has a certain specific velocity at each point. Space doesn't. A boat that uses its engine to stay at one point doesn't increase or decrease engine speed, it uses a fixed velocity to counteract the flow, it does NOT accelerate. Fixed speed = 0 acceleration (both relative to water flow and relative to shore). If a boat stays at a given point and we release rubber ducks somewhere up the river, no matter how far they were released they will flow by the boat at the same speed - the speed of flow. But objects released from different heights will fall by you at different speeds. These situations are very different. A stone falling from 10th floor and a stone falling from 3rd floor will fly by the 1st floor at very different speeds, even though both "go with the flow of space". So this illustration is very misleading, creating an illusion of understanding, but a wrong understanding. (I know you've seen these objections before, but many viewers haven't) Great work on animations though!

[@Astro_AmanJha]

Absolutely... He even said near the last that this river model is just for subtle understanding or to build a good easy picture,but not the exact reality. You highlighted the exact unmatching points...👍👍👍👍

[@kevconn441]

Now you've thrown a spanner in the works. Just when all this starts to make a glimmer of sense suddenly I'm right back where I started, confused. The stones may pass you on the 1st floor at different speeds, but they will be experiencing the same rate of acceleration. Isn't that the point?

[@timjohnson3913]

Another huge red flag with this idea is that we must assume matter is somehow attached to space, and when space is moving the matter must move along with it. It is far from clear how this interaction can work. When we travel through space, it’s not like we drag along the bits of space our matter sits on with us. Instead, traveling matter is moving into new bits of space (space atoms, if you like) as it travles.I would love to see Dialect provide the details as to why moving space would drag matter with it.

[@thedeemon]

@@kevconn441 Right, same acceleration but not same speed. Unlike a river. IMHO to get somewhat intuitive understanding of GR it's best to stick with geometry of curved spaces, a static 4D manifold, not some flowing space which may be easy to imagine but quite misleading.

[@kevconn441]

@@thedeemon I suppose you are right. Problem, for me at least, is the math is hard and it's hard to get an intuitive grip on it, if you know what I mean. I will, however, accept you are right and keep stumbling along. Thanks for the reply.

[@googleacc7243]

Wow, this is awesome explanations! Thank you!

[@jallemannen1277]

First

[@atila8623]

I have studied physics and I know how precious are your videos.❤

[@MrMeltdown]

This is the way I had to try to understand it spacetime when I read a penrose book years ago (road to reality) it was largely beyond me, but I thought I could see what he was getting at (I doubt it now) so I had to develop my own understanding (however wrong it may be as I could not invest the time to work the maths). I'm still probably wrong and working from memory so take everything I say with a bucket of salt. If space time is curved and you go with the flow (don't accelerate) you experience no weirdness. The point in space time you are at will move relative to other points in space over time dictated by the space time curvature (I think I called the time part "density" in my head for some reason). If you try to accelerate by dispersing energy/mass you are moving to another point in space time whilst the point you left is "moving" and the point you are now at is also "moving". This is where the weirdness comes in. Penrose showed this using projections of where you are if you are accelerating onto the space time where you would be if you had not accelerated, and the sum of the difference in the length of the vectors (tensors?) becomes the magnitude of all the relativistic effects, almost like you are fighting the current,

[@Michael-mf7tq]

Danke!

[@dialectphilosophy]

Bitte schön! Ihre Großzügigkeit seid für uns sehr hilfreich!

[@Michael-mf7tq]

Wonderful video. You should get all the Oskars!

[@_tyler-_-]

This series of videos has been amazing. I'm to stupid to fully grasp everything, but I'm starting to. Thank you for making these. I'm sure it's a significant workload.

[@RFQuantumLab]

In order to develop an analogical and even realistic model of space-time as a river flow-like, it is necessary to account for the "disappearance" of discrete space-time packages, as defined by Planck, in the context of "entropy" (increase in the amount of "lost" energy - Gμv = 0), after it's being drawn into the center of any mass - in question. This entails demonstrating why a singularity, by definition, is necessary for the existence of a "field". This would transform the limiting factor of the GR theory, i.e., dividing by 0 - the singularity point, into a beneficial element. Consequently, it follows that any collection of matter, such as a galaxy or a star/planet, possesses a type of black hole at its center. Furthermore, it is also necessary to account for the local conditions of space-time that allow for the creation of the properties we associate with elementary particles, such as charge, mass, spin, and other erratic movements in short distances, which are reminiscent of black hole solutions. This can only be achieved after overcoming the problem of Hawking radiation, which can be resolved by assuming that from the slowing down of time from the black hole's point of view, thus, it appears as a gradual decay from an external perspective (i.e. Proton Electron stability). Ultimately, a universal geometry with equilibrium in the "vacuum" must be established to achieve this goal.. The geometric local volume where matter Tμv is converted to space-time Gμv and space-time is converted to discrete holographic information represented boundary condition of the Black hole (the event horizon) which itself is made of discrete information on the order of Planck units. And then, finally, come to the conclusion that our observable surrounding universe is expanding rapidly because it is actually gathering more and more information across the boundary conditions, which should grow in space. By definition. Thank you,

[@juliavixen176]

It's an analogy, space isn't actually going anywhere. (see my comments elsewhere on this video) So... you know the Lagrange points? The L4 and L5 points are at a higher gravitational potential than the two orbiting masses... so... it's space flowing out from the L4 and L5 Lagrange points? (A small mass placed near one of the Lagrange points will fall away from that location.)

[@RFQuantumLab]

@@juliavixen176 Undoubtedly, the presented analogy is quite convincing. Meanwhile I’m also aware to the fact that the notion of a "flow" of space-time remains a highly speculative and theoretical one, recent advances in the understanding of gravity and space-time behavior have provided a basis for further exploration of this intriguing concept. Although the concept of space-time "flowing" is not directly observable, recent theoretical models suggest its similarity to a flow, exemplified by the phenomenon of gravitational waves. Gravitational waves result from the acceleration of massive objects, leading to space-time deformation or stretching. The concept of investigating the vacuum as a superfluid has also been proposed as a means of exploring this idea… Additionally, gravitational lensing is another related concept where the gravity of massive objects distorts the path of light. Nonetheless, these remain purely theoretical concepts without any direct observation. as yet. Thank you for your comment and the insightful reference you provided.

[@juliavixen176]

@@RFQuantumLab Gravitational waves are transverse... and transverse waves can not propagate through liquid. (Only pressure (longitudinal) waves can). The transmission medium must be a solid if transverse waves are to propagate.

[@dexter8705]

You said it yourself! Space-time... Space➡️time.

[@sirnawaz]

It's great explanation. So far for me, it's the most effective way to explain gravity which is otherwise so hard to grasp. It's still hard, but the model helps a lot. Now I've some doubts: = How does this model explain the impact of multiple celestial bodies and the gravity induced by them? How do we visualize it with the River Model? = How does this model explain and visualize planets/moons/satellites revolving around bigger celestial body but never actually fall into it? I'm waiting for your response. It'd be great if you could think of a visualization as well.

[@kiloharabaka9589]

I had an equivalent idea back then, but instead of a river I was more thinking of a "vortex of space-time". The vortex can simply explain the 1:54 counter intuitive idea of the ground accelerating upward... in fact it is accelerating by constantly changing its direction in space due to the rotation mouvement of the earth. It also simply explains why time dilation increase with gravity, and decrease with altitude by stating that in a vortex, velocity increase as you reach the centre, and decrease as you move away. Nice video, thank you. P.S : I forgot to mention that the equivalence principal is not really equivalent... in a rocket, acceleration is the same in every point of the rocket, whereas on earth, gravitation change with height.

[@Superbonker-np6iz]

Absolutely fantastic video!

[@johnfitzgerald8879]

Thank you, so very much. I have been mulling over special relativity since I first became aware of it in high school. While getting an undergraduate degree in engineering gave me better tools to work with, it has presented a hard shell that has been enough just to chip away at. General Relativity has remained far beyond by grasp. I do know enough, have just enough insight, to recognize when I am on the right path. Thank you for picking up this lowly hitchhiker and letting me ride along.

[@johnfitzgerald8879]

@@soopergoof232 The only problem I have is I can generally infer the next small step but lack sufficient skill at the mathematics of the subject to "see" two steps ahead.

[@tgcprasanna1029]

Thank you very much for simple clarification

[@michaelbyrne9246]

So, as a layperson when it comes to physics, I have been desperately trying to understand gravity (specifically Einstein's general theory of relativity) in an intuitive sense, and I think this video (along with the help of some textbooks) did it for me. That said, I have one question. I know the Earth's rotation plays into General Relativity by introducing the concept of frame dragging. I was wondering where that comes in when discussing it with this model? To me, the upward acceleration of Earth only makes sense when you factor in the Earth's rotation, but I could be wrong. That's still the only part that gets me. Love the channel. I can't get enough!

[@soopergoof232]

{QUOTE} "To me, the upward acceleration of Earth only makes sense when you factor in the Earth's rotation, but I could be wrong. That's still the only part that gets me." To be sure, the "ground accelerating up" thing *is not literal* but an allegory. The author presented it alongside the flowing-space model as two allegories of equal worth (though by now nearly 2 years later, he may have come to realize that FS *is* literal and not allegory). Frame dragging or Lense-Thirring effect for Earth is extremely miniscule, functionally non-existent due to the planet's slow rotation. It took an elaborate spaceborne experiment, NASA's Gravity Probe B, working over a year's time, to detect any drag at all. Earth's gravitational inflow pattern remains a pure "reverse starburst" for any practical purpose. Drag becomes significant with high-spin objects like millisecond pulsars, galactic-core black holes, etc. which 'torque' or curl their inflows into the familiar 'whirlpool' pattern.

[@k_dankov]

Wow, this is a great analogy and I realize here that Gravity can not be a force field as all other force fields produce accelerations on "observers" moving freely into their fields, while Gravity doesn't produce. Thanks for this awesome video!

[@emsonline4827]

fantastic explanation. thank you very much

[@BernardBrennan-wt4bk]

Very good analogies. I am able to comprehend this topic much better now.